I think we'd all agree that it's a character we begin to care about on page one. We care because she's likable, and she's got trouble. Or, as writers call it, conflict.
But what exactly does that involve? In the overall story, it means the difficulty the main character has in reaching her goals and the uncertainty of the outcome. We're not sure if she'll get what she desires so badly, so we read on.
Conflict is not just disagreement or argument. In fact, that can be annoying. But a character torn in two directions, makes us want to read on.
So if you're writing a story, force your character into something she'd never do. Make him say something he'd never say.
Write so that there's macro tension--the goal that she can't reach, and micro tension--the concern about what's said or done in the next sentence.
What do you think? What makes you keep turning the pages of a book? And what annoys you in a book?